1. Field of the Invention
The present invention relates to the field of vibratory rotation sensors such as, for example, hemispherical resonator gyroscopes (xe2x80x9cHRGxe2x80x9ds), and more particularly to a vibratory sensor where unwanted secondary harmonics are eliminated using a virtual node/antinode.
2. Description of Related Art
Vibratory sensors employ a resonating member to pick up rotation of the sensor based on the effect of Coriolis force on the resonating member. One type of vibratory sensor, used herein for example purposes only, is referred to as a hemispherical resonator gyroscope. It is to be understood that while the present discussion uses the HRG to illustrate the benefits and operation of the present invention, the present invention""s application extends to any vibratory sensor which measures oscillations of a resonating member.
Hemispherical resonator gyroscopes are known in the art for measuring an angular rate of a body about a predetermined axis. HRGs are of critical importance in space applications, such as the orienting of satellites and space vehicles. HRGs are reliable and have a long active life, making the gyro especially suited for this purpose. The gyros are typically comprised of a forcer electrode assembly, a hemispherical thin-walled quartz shell, and a pick-off electrode assembly joined together with a rare-earth metal such as indium. The unit is housed in a vacuum chamber with electrical feeds to communicate voltage signals from the gyro to a microprocessor for interpretation. The general operation of the gyroscope is discussed in the Letters Patent to Loper, Jr. et al., U.S. Pat. No. 4,951,508, which is fully incorporated herein by reference.
The hemispherical resonator 10 is a bell-shaped thin walled structure with a rim that can be made to deform from a circular profile to an elliptical profile when subjected to certain external electrical fields. The resonator is supported by an integral stem which itself is supported by the housing for the pick-off and forcer electrodes. By applying a cyclical forcing voltage, a standing wave pattern can be established in the resonator. To establish the standing wave, the hemispherical resonator is initially biased at a voltage of known magnitude, and then a varying electrical field is applied at the forcer electrodes. If the forcer electrodes apply the appropriate varying electrical field at angular intervals of 90 degrees, the resonator will flexure in a standing wave such as that shown in FIG. 1.
The primary harmonic resonating wave has four nodes a,b,c,d and four antinodes e,f,g,h around the perimeter of the resonator, alternating and equal spaced forty-five degrees apart. Nodes are points on the standing wave where displacement is a minimum, and antinodes are points on the standing wave where displacement is a maximum. Operation of the HRG requires precise tracking of the standing wave movement, which in turn requires that the location of the nodes and antinodes be accurately determined.
It is a physical property of the gyroscope that if an unrestrained resonator is rotated about an axis normal to the page (see FIG. 2), the standing wave will precess in an opposite direction to the original rotation due to Coriolis force. Moreover, the amount of the angular precess will be 0.3 times the angular displacement of the resonator, where 0.3 is a geometric property of the resonator""s hemispherical shape and holds constant for any rotation angle and any rotation rate. For example, if the resonator of FIG. 1 is rotated ninety degrees in the counter-clockwise direction, as indicated by the angular displacement of the notch 20, the standing wave will precess twenty-seven degrees clockwise as shown in FIG. 2. In this manner when an HRG is rotated about its primary axis, by measuring the change in the angular position of the standing wave information about the rotation of the HRG can be determined.
The position of the standing wave both before and after the rotation of the gyroscope is determined by the pick-off electrodes positioned about the external annular component of the housing. By measuring the capacitance across the gap formed between the pick-off electrodes and the resonator, the distance across the gap can be accurately determined. This information is processed by a microprocessor in a manner such that the exact position of the standing wave is determined. By measuring the change in position of the standing wave, the rotation of the gyro can readily be determined.
HRGs operate in one of two modesxe2x80x94whole angle mode and force rebalance mode. In whole angle mode, the standing wave is allowed to precess unhindered under the influence of the Coriolis force caused by the rotation of the gyro as just described. The instantaneous position of the standing wave is evaluated by computing the arctangent of the ratio of the amplitude of the two pickoff signals. In the whole angle mode the gyro""s dynamic range is limited solely by the resolution and processing of the pick-off signal estimation.
In the force rebalance mode, the standing wave is constrained such that it does not precess under the influence of the Coriolis force, and the magnitude of the restraining force is used to calculate the rotation rate of the gyro. In this mode, an additional forcing signal is included which holds the standing wave at a fixed azimuthal location. The amount of force necessary to maintain the standing wave fixed is proportional to the input rotational rate. For force rebalance gyros, the case-oriented control and readout processing is eliminated, and the output noise performance can be optimized because the dynamic range requirements of the pick-off signal estimation are greatly reduced.
In the force rebalance mode, four separate control mechanisms are necessary. The first control mechanism is the phase-lock loop, which is necessary to track the natural frequency and phase of the high Q resonance. This loop provides a timing reference for the other readout and drive mechanisms. The second control mechanism is the amplitude control loop, which establishes and maintains the required stable standing wave amplitude. The third control mechanism is the quadrature control loop, which is used to eliminate the small frequency mismatch between the two principal axes of flexure. The final control mechanism is the rate control loop, which is attributed only to the force rebalance mode, and holds the standing wave in a fixed position while measuring the inertial rate directly through the applied closed-loop forcing.
The phase-lock, amplitude control, and quadrature loops are required for both whole angle mode and force rebalance mode. The amplitude control and the phase-lock loops maintain the flexing amplitude and timing reference, respectively. These processes are associated with the antinode axis pickoffs and forcers. The nominal flexing amplitude defines the stored momentum and the rate scale factor in the HRG in the force rebalance mode. The phase-locked loop is necessary to track the free-running oscillation of the resonator so that the demodulation and drive functions can be synchronized to the narrowband resonance. The quadrature and rate control loops use independent forcers to drive the nodal pickoff amplitude components to zero. The quadrature control loop suppresses the quadrature-mode vibration which develops because of the small frequency mismatch between the two axes.
The rate control loop uses the rate drive to null the in-phase nodal amplitude component, i.e., standing wave deflection. FIG. 3 is a representation of a rate control loop, where the box 30 represents a model of the HRG mechanics. The model includes a scale factor K which converts volts to an electrostatic force that cancels the Coriolis force due to an inertial input, and the resultant difference force to dynamic response P(s) of the in-phase nodal amplitude yi. The difference force includes a thermal noise component xcexa9TN as well as a bias component xcexa9B. The input from the HRG pickoff is amplified 40 and converted to a digital signal 50 where a microprocessor 60 can analyze the signal and output a rate estimate R. The digital rate estimate is supplied to the digital to analog converter which generates a HRG phase synchronous signal of the necessary amplitude to maintain Yi at zero. The analog signal is amplified 80 and summed with the forcer electrode voltage signal VDN and the signal is returned to the model 30 for further processing.
In the force rebalance mode, the primary vibration wave or patter, i.e., the 2N vibration pattern, is constrained to be fixed with respect to the HRG. The present HRG constrains the standing wave such that a node is fixed directly under a pickoff electrode. Since the signal is reduced to a theoretical minimum directly under the node, the signal can be amplified for greater precision. It is this amplified signal VPN which is the input to the rate control loop, and is used to control the forcing command to maintain this signal at xe2x80x9czero.xe2x80x9d
The shortcoming with the methodology just described is that the standing wave in the resonator has harmonics in addition to the 2N vibration pattern. Of these, the secondary harmonic is the most important, because the secondary harmonic has a maximum located at the 2N vibration pattern node. Thus, where the signal is ideally supposed to be zero there is a maximum contribution from the secondary harmonic, which limits the amplification of the signal. In addition, the pickoff capacitor has a finite size, and experiences the displacement of the resonator directly under the entire surface of the electrode. Because of the spherical geometry of the pick-off and the shape that the resonator takes when it flexes, when the node is directly in the center of the pickoff there is an average displacement between the flexing resonator and the pickoff at twice the primary frequency. This second harmonic prevents a high amplification of the signal.
The present invention seeks to overcome the shortcomings of the prior art vibratory sensors by creating a virtual node and antinode to evaluate the standing wave inertial signal. In a preferred embodiment of the present invention, a virtual node is created by constraining the actual antinode of the 2N vibration pattern equally spaced between two pickoff electrodes. The signals from these two pickoff electrodes are then both summed and differenced by appropriate electronic circuitry to create a virtual antinode and a virtual node, respectively. The virtual node is created because the two signals equally spaced from the actual antinode both include an equal contribution from the 2N flexing mode and the secondary harmonic, such that when the two signals are differenced the resultant signal has a very small output. Similarly, the virtual antinode comprises the peak radial displacement of the 2N flexing mode and the secondary harmonic flexing mode. The virtual node is now reduced to the level of electrode manufacturing differences, which is small enough to permit high amplification without the need for frequency shifting and filtering. While the virtual antinode includes two contributions from the secondary harmonic, the value of the secondary harmonic is less than one percent (1%) on average of the primary vibration mode and hence the contribution of the secondary harmonic will not significantly impact the dynamic range of the analog-to-digital conversion when sampling the virtual antinode.